Answer to Question #186082 in Statistics and Probability for mya

Question

4. Mrs. Dela Cruz gave a 50-item test to her 115 Grade 12 students.

The result of the exam shows an average score of 36 with a standard deviation

of 2.7. Suppose Mrs. Dela Cruz repeatedly took 33 samples and calculated the

sample mean from each sample. complete solution

 

4.1. Find the mean of the sample means.

4.2. Compute for the standard error of the

sample mean.

4.3. Determine the shape of the sampling

distribution of the sample mean.

Answer 1

Given, Population mean $\mu=36$

Standard deviation $\sigma=2.7$

Now cruz takes a sample of $n=33$

4.1 Then mean of sample mean $\bar{x}=\mu=36$

4.2 Standard error of sample mean s$=\dfrac{\sigma}{\sqrt{n}}$

$=\dfrac{2.7}{\sqrt{33}}=\dfrac{2.7}{5.74}=0.47$

4.3 The sampling distribution of the mean has a shape approaching the shape of the familiar bell curve.